Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <iostream>
#include <cstdio>
using namespace std;
int n, a[200010], p[200010];
int main () {
    scanf ("%d", &n);
    for (int i = 1; i <= n; i++) scanf ("%d", &a[i]), p[a[i]] = i;
    int T = 0, f = 0;
    for (int i = n - 1; i >= 1; i--) {
        if (!T) {
            if (p[i] > p[i + 1]) T = 1, f = i + 1;
            continue;
        }
        if (p[f] <= p[i] && p[i] <= p[i + 1]) continue;
        if (p[i] <= p[i + 1] && p[i + 1] <= p[f]) continue;
        if (p[i + 1] <= p[f] && p[f] <= p[i]) continue;
        T++, f = i + 1;
    }
    printf ("%d\n", T);
    return 0;
}